For weeks now, as Washington slouches toward a New Year’s deadline for averting a potentially calamitous combination of automatic tax increases and sharp spending cuts, Barack Obama has insisted that any agreement to avoid the so-called fiscal cliff must include an agreement to raise tax rates on top earners. House Speaker John Boehner, the Republican negotiator charged with cutting a deal with the President, has yet to publicly accede to that demand. But in recent days, Republicans have begun bowing to the reality that the GOP has a weak position in the skirmish over tax rates. Obama campaigned on higher rates for the richest Americans and won. If no pact is forged, rates will rise for all taxpayers — and polls suggest Republicans will bear the bulk of the blame. Which is why a few influential Republicans have suggested that since the party will be forced to cave to Obama’s demands on tax rates, it should do so now, and retrench for the battles to come next year, when the GOP will have more leverage.

That doesn’t mean Obama and Boehner will be able to prevent the country from toppling over the cliff. As a counterweight to a tax hike that is anathema to his members, Boehner needs to extract concessions from Democrats in the form of cuts to entitlement programs. Obama has expressed willingness to cut a deal that scales back such programs; during the misbegotten talks to craft a far-reaching deficit-reduction plan last summer, he put some $350 billion in cuts to federal health programs over the next decade on the table, so long as they accompanied sizable revenue increases achieved through rate increases or tax reform. The White House has been disciplined about keeping the substance of the President’s conversations with Boehner private, but having gone that far once, he is probably prepared to offer something similar again if the other pieces of the puzzle are in place.

But many Democrats are loath to agree to entitlement cuts. That’s partly because of their ideological convictions, partly because they wield the issue as a perennial political cudgel, and partly because they believe going over the cliff will lock in the tax hikes on the wealthy they sought in the first place. At which point, the thinking goes, the party could introduce a bill to cut taxes for 98% of Americans that Republicans would be hard-pressed not to go along with. “To blame the three programs that we’re talking about — Medicare, Medicaid and Social Security — as the drivers of this deficit is a mistake,” Democratic Representative Raul Grijalva said Sunday on ABC’s “This Week.”

In response to Obama’s offer, Boehner has proposed to cut $600 billion from federal health programs over the next 10 years. The substance of those cuts are shrouded. But they could involve some combination of a change to the Medicare eligibility age, means-testing benefits or changes to the way the government calculates inflation, which could result in lower payments to recipients of Social Security.

Obama has been tentatively receptive to some of these ideas in the past. And the framework for an agreement between and he and Boehner isn’t hard to discern. Obama has asked for $1.6 trillion in new tax revenue, while Boehner countered with $800 billion. The two are a few hundred billion apart on entitlement cuts. The two men could meet somewhere in the middle on both, call it a down payment on the $4 trillion in deficit reduction both seek over the next decade, and agree to hash out the logistics of tax reform next fall, in what would surely be an equally infuriating exercise.

But neither leader rules by fiat, and each has quarrelsome members of his own party bristling about a compromise. Some Republicans are deluded about the damage a failure to forge a deal would inflict, just as they refused to believe warnings about the debt limit last summer. Even Democrats who admit they will need to give ground on entitlements to forge a deal would prefer to cut entitlements in other ways and at lower levels. Between the faction of Democrats resistant to cut for health beneficiaries and the faction of Republicans who believe that the economic turmoil of going over the cliff is worth absorbing for a whack at the deficit, Obama and Boehner may find it tough to muster the votes to thread a deal through Congress. And negotiators are running out of time.